Part III - Prominent classes of strategic form games

Summary

INTRODUCTION

In the previous chapters we defined the basic solution concepts for strategic form games – from those relying on considerations of dominance to the notion of Nash equilibrium which hinges on a concept of stability. It is now time to explore important classes of strategic form games and to analyze their properties.

Chapter 7 addresses a twofold classification: games of cooperation vs. games of conflict, and games with strategic complements vs. games with strategic substitutes. The first distinction asks whether each player would have preferred her rivals to increase the intensity of their action (games of cooperation) or decrease it (games of conflict). The second distinction asks whether, upon an increase in the intensity of the rivals’ action, the player herself would have preferred to increase the intensity of her own action (strategic complements) or decrease it (strategic substitutes); or, in other words, whether the reaction function of the player is increasing (the case of strategic substitutes) or decreasing (strategic complements).

Somewhat surprisingly, these two dimensions of classification are independent of one another, and each of the four combinations of cooperation/conflict and strategic complements/substitutes is possible. The partnership game, presented already in Chapter 6, is an example of a game of cooperation with strategic complements. The first example in that chapter, that of a public good game, is of cooperation with strategic substitutes. This game is analyzed in detail, showing, first, that its Nash equilibrium is inefficient – i.e. that all players would have preferred to play a profile of strategies in which they all invest more than at the Nash equilibrium. Unfortunately, such a unanimously preferable investment profile is not a Nash equilibrium and hence does not constitute a stable, self-sustaining agreement. Furthermore, we show that the larger the group of players, the more inefficient the Nash equilibrium becomes.